Selecting the Runoff Pair
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Critical Strategies Under Approval Voting: Who Gets Ruled in and Ruled Out
Critical Strategies Under Approval Voting: Who Gets Ruled In And Ruled Out Steven J. Brams Department of Politics New York University New York, NY 10003 USA [email protected] M. Remzi Sanver Department of Economics Istanbul Bilgi University 80310, Kustepe, Istanbul TURKEY [email protected] January 2005 2 Abstract We introduce the notion of a “critical strategy profile” under approval voting (AV), which facilitates the identification of all possible outcomes that can occur under AV. Included among AV outcomes are those given by scoring rules, single transferable vote, the majoritarian compromise, Condorcet systems, and others as well. Under each of these systems, a Condorcet winner may be upset through manipulation by individual voters or coalitions of voters, whereas AV ensures the election of a Condorcet winner as a strong Nash equilibrium wherein voters use sincere strategies. To be sure, AV may also elect Condorcet losers and other lesser candidates, sometimes in equilibrium. This multiplicity of (equilibrium) outcomes is the product of a social-choice framework that is more general than the standard preference-based one. From a normative perspective, we argue that voter judgments about candidate acceptability should take precedence over the usual social-choice criteria, such as electing a Condorcet or Borda winner. Keywords: approval voting; elections; Condorcet winner/loser; voting games; Nash equilibrium. Acknowledgments. We thank Eyal Baharad, Dan S. Felsenthal, Peter C. Fishburn, Shmuel Nitzan, Richard F. Potthoff, and Ismail Saglam for valuable suggestions. 3 1. Introduction Our thesis in this paper is that several outcomes of single-winner elections may be socially acceptable, depending on voters’ individual views on the acceptability of the candidates. -
Low-Magnitude Proportional Electoral Systems
The Electoral Sweet Spot: Low-Magnitude Proportional Electoral Systems John M. Carey Dartmouth College Simon Hix London School of Economics and Political Science Can electoral rules be designed to achieve political ideals such as accurate representation of voter preferences and accountable governments? The academic literature commonly divides electoral systems into two types, majoritarian and proportional, and implies a straightforward trade-off by which having more of an ideal that a majoritarian system provides means giving up an equal measure of what proportional representation (PR) delivers. We posit that these trade-offs are better characterized as nonlinear and that one can gain most of the advantages attributed to PR, while sacrificing less of those attributed to majoritarian elections, by maintaining district magnitudes in the low to moderate range. We test this intuition against data from 609 elections in 81 countries between 1945 and 2006. Electoral systems that use low-magnitude multimember districts produce disproportionality indices almost on par with those of pure PR systems while limiting party system fragmentation and producing simpler government coalitions. An Ideal Electoral System? seek to soften the representation-accountability trade-off and achieve both objectives. For example, some electoral t is widely argued by social scientists of electoral sys- systems have small multimember districts, others have tems that there is no such thing as the ideal electoral high legal thresholds below which parties cannot win system. Although many scholars harbor strong pref- seats, while others have “parallel” mixed-member sys- I tems, where the PR seats do not compensate for dispro- erences for one type of system over another, in published work and in the teaching of electoral systems it is standard portional outcomes in the single-member seats. -
Brake & Branscomb
Colorado Secretary of State 8/3/2021 Election Rulemaking These proposed edits to the SOS draft are contributed by Emily Brake (R) and Harvie Branscomb (D), and approved by Frank Atwood, Chair of the Approval Voting Party This document may be found on http://electionquality.com version 1.3 8/10/2021 15:50 Only portions of the recent draft rule text are included here with inline edits and comments highlighted as follows: Comments are highlighted in yellow. INSERTS ARE IN GREEN AND LARGE FONT deletions are in red and include strikeout Other indications of strikeout are from the original tabulation process 2.13.2 In accordance with section 1-2-605(7), C.R.S., no later than 90 days following a General Election, the county clerk in each county must SECRETARY OF STATE WILL PROPOSE cancelLATION OF the registrations of electors TO EACH COUNTY CLERK: [Comment: SOS taking responsibility from counties will lead to less verification and less resilience. The SOS office has not been subject to watcher access but will be as various steps of the conduct of election are taken over.] (a) Whose records have been marked “Inactive – returned mail”, “Inactive – undeliverable ballot”, or “Inactive – NCOA”; AND (b) Who have been mailed a confirmation card; and (c) Who have since THEREAFTER failed to vote in two consecutive general elections. New Rule 2.13.3, amendments to current Rule 2.13.3, repeal of 2.13.5, and necessary renumbering:VOTERS WHO REQUEST AN EMERGENCY BALLOT BE SENT TO THEM ELECTRONICALLY MUST BE DIRECTED BY THE COUNTY CLERK TO THE ONLINE BALLOT DELIVERY SYSTEM MAINTAINED BY THE SECRETARY OF STATE TO RECEIVE THEIR BALLOT ELECTRONICALLY. -
A Generalization of the Minisum and Minimax Voting Methods
A Generalization of the Minisum and Minimax Voting Methods Shankar N. Sivarajan Undergraduate, Department of Physics Indian Institute of Science Bangalore 560 012, India [email protected] Faculty Advisor: Prof. Y. Narahari Deparment of Computer Science and Automation Revised Version: December 4, 2017 Abstract In this paper, we propose a family of approval voting-schemes for electing committees based on the preferences of voters. In our schemes, we calcu- late the vector of distances of the possible committees from each of the ballots and, for a given p-norm, choose the one that minimizes the magni- tude of the distance vector under that norm. The minisum and minimax methods suggested by previous authors and analyzed extensively in the literature naturally appear as special cases corresponding to p = 1 and p = 1; respectively. Supported by examples, we suggest that using a small value of p; such as 2 or 3, provides a good compromise between the minisum and minimax voting methods with regard to the weightage given to approvals and disapprovals. For large but finite p; our method reduces to finding the committee that covers the maximum number of voters, and this is far superior to the minimax method which is prone to ties. We also discuss extensions of our methods to ternary voting. 1 Introduction In this paper, we consider the problem of selecting a committee of k members out of n candidates based on preferences expressed by m voters. The most common way of conducting this election is to allow each voter to select his favorite candidate and vote for him/her, and we select the k candidates with the most number of votes. -
The Case for Electoral Reform: a Mixed Member Proportional System
1 The Case for Electoral Reform: A Mixed Member Proportional System for Canada Brief by Stephen Phillips, Ph.D. Instructor, Department of Political Science, Langara College Vancouver, BC 6 October 2016 2 Summary: In this brief, I urge Parliament to replace our current Single-Member Plurality (SMP) system chiefly because of its tendency to distort the voting intentions of citizens in federal elections and, in particular, to magnify regional differences in the country. I recommend that SMP be replaced by a system of proportional representation, preferably a Mixed Member Proportional system (MMP) similar to that used in New Zealand and the Federal Republic of Germany. I contend that Parliament has the constitutional authority to enact an MMP system under Section 44 of the Constitution Act 1982; as such, it does not require the formal approval of the provinces. Finally, I argue that a national referendum on replacing the current SMP voting system is neither necessary nor desirable. However, to lend it political legitimacy, the adoption of a new electoral system should only be undertaken with the support of MPs from two or more parties that together won over 50% of the votes cast in the last federal election. Introduction Canada’s single-member plurality (SMP) electoral system is fatally flawed. It distorts the true will of Canadian voters, it magnifies regional differences in the country, and it vests excessive political power in the hands of manufactured majority governments, typically elected on a plurality of 40% or less of the popular vote. The adoption of a voting system based on proportional representation would not only address these problems but also improve the quality of democratic government and politics in general. -
1 Introduction 2 Condorcet and Borda Tallies
1 Introduction General introduction goes here. 2 Condorcet and Borda Tallies 2.1 Definitions We are primarily interested in comparing the behaviors of two information aggregation methods, namely the Condorcet and Borda tallies. This interest is motivated by both historical and practical concerns: the relative merits of the two methods have been argued since the 18th century, and, although variations on the Borda tally are much more common in practice, there is a significant body of theoretical evidence that the Condorcet tally is in many cases superior. To begin, we provide formal definitions of both of these methods, and of a generalized information aggregation problem. An information aggregation problem, often referred to simply as a voting problem, is a problem which involves taking information from a number of disparate sources, and using this information to produce a single output. Problems of this type arise in numerous domains. In political science, they are common, occurring whenever voters cast votes which are used to decide 1 the outcome of some issue. Although less directly, they also occur in fields as diverse as control theory and cognitive science. Wherever there is a system which must coalesce information from its subsystems, there is potentially the need to balance conflicting information about a single topic. In any such circumstance, if there is not reason to trust any single source more than the others, the problem can be phrased as one of information aggregation. 2.1.1 Information Aggregation Problems To facilitate the formalization of these problems, we only consider cases in which a finite number of information sources (which shall henceforth be re- ferred to as voters) provide information regarding some contested issue. -
THE SINGLE-MEMBER PLURALITY and MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election
THE SINGLE-MEMBER PLURALITY AND MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election by James C. Anderson A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Arts in Political Science Waterloo, Ontario, Canada, 2006 © James C. Anderson 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Library and Bibliotheque et Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-23700-7 Our file Notre reference ISBN: 978-0-494-23700-7 NOTICE: AVIS: The author has granted a non L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce,Canada de reproduire, publier, archiver, publish, archive, preserve, conserve,sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet,distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non sur support microforme, papier, electronique commercial purposes, in microform,et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. -
Are Condorcet and Minimax Voting Systems the Best?1
1 Are Condorcet and Minimax Voting Systems the Best?1 Richard B. Darlington Cornell University Abstract For decades, the minimax voting system was well known to experts on voting systems, but was not widely considered to be one of the best systems. But in recent years, two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems. Comments invited. [email protected] Copyright Richard B. Darlington May be distributed free for non-commercial purposes Keywords Voting system Condorcet Minimax 1. Many thanks to Nicolaus Tideman, Andrew Myers, Sharon Weinberg, Eduardo Marchena, my wife Betsy Darlington, and my daughter Lois Darlington, all of whom contributed many valuable suggestions. 2 Table of Contents 1. Introduction and summary 3 2. The variety of voting systems 4 3. Some electoral criteria violated by minimax’s competitors 6 Monotonicity 7 Strategic voting 7 Completeness 7 Simplicity 8 Ease of voting 8 Resistance to vote-splitting and spoiling 8 Straddling 8 Condorcet consistency (CC) 8 4. Dismissing eight criteria violated by minimax 9 4.1 The absolute loser, Condorcet loser, and preference inversion criteria 9 4.2 Three anti-manipulation criteria 10 4.3 SCC/IIA 11 4.4 Multiple districts 12 5. Simulation studies on voting systems 13 5.1. Why our computer simulations use spatial models of voter behavior 13 5.2 Four computer simulations 15 5.2.1 Features and purposes of the studies 15 5.2.2 Further description of the studies 16 5.2.3 Results and discussion 18 6. -
An Electoral System Fit for Today? More to Be Done
HOUSE OF LORDS Select Committee on the Electoral Registration and Administration Act 2013 Report of Session 2019–21 An electoral system fit for today? More to be done Ordered to be printed 22 June 2020 and published 8 July 2020 Published by the Authority of the House of Lords HL Paper 83 Select Committee on the Electoral Registration and Administration Act 2013 The Select Committee on the Electoral Registration and Administration Act 2013 was appointed by the House of Lords on 13 June 2019 “to consider post-legislative scrutiny of the Electoral Registration and Administration Act 2013”. Membership The Members of the Select Committee on the Electoral Registration and Administration Act 2013 were: Baroness Adams of Craigielea (from 15 July 2019) Baroness Mallalieu Lord Campbell-Savours Lord Morris of Aberavon (until 14 July 2019) Lord Dykes Baroness Pidding Baroness Eaton Lord Shutt of Greetland (Chairman) Lord Hayward Baroness Suttie Lord Janvrin Lord Wills Lord Lexden Declaration of interests See Appendix 1. A full list of Members’ interests can be found in the Register of Lords’ Interests: http://www.parliament.uk/mps-lords-and-offices/standards-and-interests/register-of-lords- interests Publications All publications of the Committee are available at: https://committees.parliament.uk/committee/405/electoral-registration-and-administration-act- 2013-committee/publications/ Parliament Live Live coverage of debates and public sessions of the Committee’s meetings are available at: http://www.parliamentlive.tv Further information Further information about the House of Lords and its Committees, including guidance to witnesses, details of current inquiries and forthcoming meetings is available at: http://www.parliament.uk/business/lords Committee staff The staff who worked on this Committee were Simon Keal (Clerk), Katie Barraclough (Policy Analyst) and Breda Twomey (Committee Assistant). -
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy (B), Carla (C), Doris (D), and Emilia (E) are candidates for an open Student Government seat. There are 110 voters with the preference lists below. 36 24 20 18 8 4 A E D B C C B C E D E D C B C C B B D D B E D E E A A A A A Who wins the election if the method used is: a) plurality? b) plurality with runoff? c) sequential pairwise voting with agenda ABEDC? d) Hare system? e) Borda count? 2. What is the minimum number of votes needed for a majority if the number of votes cast is: a) 120? b) 141? 3. Consider the following preference lists: 1 1 1 A C B B A D D B C C D A If sequential pairwise voting and the agenda BACD is used, then D wins the election. Suppose the middle voter changes his mind and reverses his ranking of A and B. If the other two voters have unchanged preferences, B now wins using the same agenda BACD. This example shows that sequential pairwise voting fails to satisfy what desirable property of a voting system? 4. Consider the following preference lists held by 5 voters: 2 2 1 A B C C C B B A A First, note that if the plurality with runoff method is used, B wins. Next, note that C defeats both A and B in head-to-head matchups. This example shows that the plurality with runoff method fails to satisfy which desirable property of a voting system? 5. -
Absolute Voting Rules Adrian Vermeule
University of Chicago Law School Chicago Unbound Coase-Sandor Working Paper Series in Law and Coase-Sandor Institute for Law and Economics Economics 2005 Absolute Voting Rules Adrian Vermeule Follow this and additional works at: https://chicagounbound.uchicago.edu/law_and_economics Part of the Law Commons Recommended Citation Adrian Vermeule, "Absolute Voting Rules" (John M. Olin Program in Law and Economics Working Paper No. 257, 2005). This Working Paper is brought to you for free and open access by the Coase-Sandor Institute for Law and Economics at Chicago Unbound. It has been accepted for inclusion in Coase-Sandor Working Paper Series in Law and Economics by an authorized administrator of Chicago Unbound. For more information, please contact [email protected]. CHICAGO JOHN M. OLIN LAW & ECONOMICS WORKING PAPER NO. 257 (2D SERIES) Absolute Voting Rules Adrian Vermeule THE LAW SCHOOL THE UNIVERSITY OF CHICAGO August 2005 This paper can be downloaded without charge at: The Chicago Working Paper Series Index: http://www.law.uchicago.edu/Lawecon/index.html and at the Social Science Research Network Electronic Paper Collection: http://ssrn.com/abstract_id=791724 Absolute Voting Rules Adrian Vermeule* The theory of voting rules developed in law, political science, and economics typically compares simple majority rule with alternatives, such as various types of supermajority rules1 and submajority rules.2 There is another critical dimension to these questions, however. Consider the following puzzles: $ In the United States Congress, the votes of a majority of those present and voting are necessary to approve a law.3 In the legislatures of California and Minnesota,4 however, the votes of a majority of all elected members are required. -
Stable Voting
Stable Voting Wesley H. Hollidayy and Eric Pacuitz y University of California, Berkeley ([email protected]) z University of Maryland ([email protected]) September 12, 2021 Abstract In this paper, we propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head majority comparison, then A should still win in the election with B included (unless there is another candidate A0 who has the same kind of claim to winning, in which case a tiebreaker may choose between A and A0). We call this principle Stability for Winners (with Tiebreaking). Stable Voting satisfies this principle while also having a remarkable ability to avoid tied outcomes in elections even with small numbers of voters. 1 Introduction Voting reform efforts in the United States have achieved significant recent successes in replacing Plurality Voting with Instant Runoff Voting (IRV) for major political elections, including the 2018 San Francisco Mayoral Election and the 2021 New York City Mayoral Election. It is striking, by contrast, that Condorcet voting methods are not currently used in any political elections.1 Condorcet methods use the same ranked ballots as IRV but replace the counting of first-place votes with head- to-head comparisons of candidates: do more voters prefer candidate A to candidate B or prefer B to A? If there is a candidate A who beats every other candidate in such a head-to-head majority comparison, this so-called Condorcet winner wins the election.